Crowdsourcing can collect many diverse ideas by prompting ideators individually, but this can generate redundant ideas. Prior methods reduce redundancy by presenting peers ideas or peer-proposed prompts, but these require much human coordination. We introduce Directed Diversity, an automatic prompt selection approach that leverages language model embedding distances to maximize diversity. Ideators can be directed towards diverse prompts and away from prior ideas, thus improving their collective creativity. Since there are diverse metrics of diversity, we present a Diversity Prompting Evaluation Framework consolidating metrics from several research disciplines to analyze along the ideation chain - prompt selection, prompt creativity, prompt-ideation mediation, and ideation creativity. Using this framework, we evaluated Directed Diversity in a series of a simulation study and four user studies for the use case of crowdsourcing motivational messages to encourage physical activity. We show that automated diverse prompting can variously improve collective creativity across many nuanced metrics of diversity.